Question

D and E are points on the sides AB and AC respectively of a ΔABC. In the following cases, determine whether DE || BC or not. 

AB = 11.7 cm, AC = 11.2 cm, BD = 6.5 cm and AE = 4.2 cm.

Answer 1

We have:
AB = 11.7 cm, DB = 6.5 cm
Therefore,
AD = 11.7 -6.5 = 5.2 cm
Similarly,
AC = 11.2 cm, AE = 4.2 cm
Therefore,
EC = 11.2 – 4.2 = 7 cm 
Now,
`(AD)/(DB)=5.2/6.5=4/5`
`(AE)/(EC)=4.2/7`
Thus,`(AD)/(DB)≠ (AE)/(EC)`
Applying the converse of Thales’ theorem,
We conclude that DE is not parallel to BC.